The preliminary results were based on a count of more than 91 per cent of the votes cast in 16 of Iraq's 18 provinces.
Early results from Iraq's electoral commission place al-Sadr and Prime Minister Haider al-Abadi as the two leading politicians in the race - the fourth election since the USA invasion in 2003 brought down Saddam Hussein's dictatorship, and the first after Iraq's three-year war against ISIS, which ended last December.
On Monday evening, Abadi called for all parties and citizens to respect the results of the May 12 election. The result is that long after the elections have finished, the embittered Iraqi divide will be bickering and jostling for months to form a government.
Abadi encouraged all political parties and electoral lists that have concerns over the polling process to use legal procedures to contest the preliminary elections results.
Most billboards bore faces that have been around since 2003.
Voter turnout was 44.5%, had voted more than 10 million Iraqis. However, ahead of Saturday's national election, he distanced himself from Iran.
The reason appeared to be a mix of anger and cynicism. Iraq's many political factions mean a government may only be formed after drawn out negotiations.
How the vote tally translates into parliamentary seats will be announced later this week, Iraq's election commission said. "I did not find any other choice to express my rejection except to boycott".
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"The list of candidates Abadi put forward was full of people who have been in power for 15 years and were accused of having done nothing during that time", said Hashimi.
Abadi was viewed as a frontrunner before the election. "Our policy is to prevent it", he said. The news of al-Sadr's lead was widely reported by many major media outlets.
Politicians closely aligned to neighboring Iran appear to have gathered weaker support than expected.
The head of the list is Hadi al-Ameri, a long-time ally of Tehran, whose forces ended up battling alongside the U.S. to oust the jihadists. If it can summon the focus and diplomatic resources. there's an opportunity to reinforce the incipient shift toward nonsectarian politics built around support for Iraqi sovereignty - including from Iran.
Iraq has been ranked among the world's most corrupt countries, with high unemployment, poverty, weak public institutions and crumbling infrastructure despite high oil revenues for many years.
According to preliminary results on Kurdish outlet Rudaw, al-Sadr's coalition, Iraqi Prime Minister Haidar al-Abadi's Nasr (Victory) Coalition, and Hadi al-Amiri's Fatih (Conquest) Coalition are now believed to be in a three-way tie.
Sadr, usually stern-faced, joked about the diplomat's ring. That possibility might send chills through many Americans, who recall the deadly attacks his followers launched against US soldiers during the 2000s.
Al-Sadr's Mahdi army was once heavily reliant on Iran. That would be a sharp break from his previous image as a fiery rabble-rouser. Since the first elections following Saddam's ouster, the Shiite majority has held the position of prime minister, while the Kurds have held the presidency and the Sunnis have held the post of parliament speaker.